Detectives investigating crimes aim to establish who had the means, motive, and opportunity which usually narrows down the field of suspects. The same rules apply to political leaks. The intriguing curiosity in the case of the now infamous memo regarding the discussions with French diplomats held by Nicola Sturgeon is that the field of culprits is already narrowed down but the motives are oddly obscure.

Surely friendly governments do not interfere in the domestic politics of another?

Discerning the motivation is not made any easier by the complete denial of the veracity of the key part of the memo by both the French diplomats and the SNP government. The key line in it is that Ms Sturgeon “confessed that she’d rather see David Cameron remain as prime minister (and didn’t see Ed Miliband as PM material)”.

Ms Sturgeon says these 18 words are “100 per cent untrue” and the French diplomat says Ms Sturgeon “did not touch on her political preferences for the next British prime minister, not at all.”

That means there is no end of mystery here. If the denials are true, why did these apparently invented words appear in an internal memo we know to have been written by a UK government civil servant working in the Scotland Office after a conversation with Pierre-Alain Coffinier, France’s Consul-General in Edinburgh, who was at this meeting?

Are they just a sheer invention? Unlikely, as making things up can end a civil servant’s career. Did Mr Coffinier make them up? Again unlikely, as diplomacy and diplomatic careers depend on very accurate noting and transmission of words and intentions.

But the rest of the memo makes it clear that there was a lively discussion about the election and Scottish politics as the French ambassador Sylvie Bermann “was quite struck by the Labour v SNP political debate in Scotland as opposed to the different Westminster dynamic”. It is therefore possible that Mr Coffinier was given an inch and extended it to a mile in his interpretation of this discussion and relayed this impression to the Scotland Office official, who also may have over-interpreted it.

But this too seems odd. Mr Coffinier’s job is to brief the French government, not the UK government, about Scottish politics. And it won’t do Mr Coffinier’s chances of getting confidential briefings from the Scottish government much good if its ministers and officials think that he is passing everything on to the UK government.

So I am inclined to think that this is a case of some smallish points in what seems to have been a fairly intense discussion being over-elaborated – a case of two and two being put together to make eight.

Ms Sturgeon has, of course, demanded that the UK government identify who put this double-counting into the public domain, a request to which the head of the UK civil service, Sir Jeremy Heywood, has agreed. This, however, distracts from the central political question.

The leak was designed to undermine the SNP and benefit other parties, particularly Labour. And is it possible that SNP leaders, despite their public stance of favouring a Labour government, do actually privately prefer the prospect of a Conservative one led by David Cameron? If the memo was an over-elaboration, this has to remain as the grain of truth in the original discussion which the memo has turned into a wheat field.

Well, in terms of Scotland’s national interest, Labour is pledged to less austerity than are the Tories. And if keeping as much spending power in Scottish pockets as possible is the SNP’s main and only objective, then the memo must be false.

But national interest is not the same as party interest. And the SNP’s prime objective is to use the election outcome to wrest as much economic and tax power as possible from Westminster. Here, it is a provable fact that David Cameron’s premiership has served the SNP very well.

He conceded one set of powers through the Scotland Act 2012’s implementation of the Calman Commission proposals, is well down the track of implementing the Smith Commission’s plans for further devolution, and conceded the independence referendum.

In the power-grab game, Mr Cameron has been an absolute pushover, while an evidently more reluctant Labour needed a big push from Gordon Brown before it matched the Tories’ generosity. The conclusion seems inescapable – the SNP stands a much better chance of screwing more powers for the Scottish Parliament out of Mr Cameron than from Mr Miliband.

And a continued Cameron premiership also serves the main dynamic pushing the SNP forward – that it is ideally placed as in government in Scotland and in opposition, indeed perceived as the principle opposition, to Westminster. Mr Cameron staying in Downing Street guarantees Ms Sturgeon a much easier Holyrood re-election in 2016 than if Mr Miliband was to move into power.

But there is one other government interest here – that of the French government served by the diplomats at the meeting with Ms Sturgeon. What government would president François Hollande like to see in London?

Crude conventional wisdom is that he would prefer to see Mr Cameron, who would then hold an in-out European Union referendum resulting in Britain quitting the EU (which, incidentally, would also suit the SNP and its independence quest), ridding Europe of annoying Anglo-Saxon influence.

But that is too crude. A “Brexit” also means that French payments to the EU would have to rise and may even threaten the break-up of the EU, the creation of which is France’s greatest diplomatic triumph. A Miliband premiership, on the other hand, averts both those problems, rids the European Council of Germany’s staunchest pro-austerity ally, and thereby helps his own re-election chances in 2017.

But surely friendly governments do not interfere in the domestic politics of another? Like hell they don’t. Mr Hollande is unlikely to have forgotten that Mr Cameron endorsed his right-wing rival Nicholas Sarkozy in the 2012 French election and might be quite happy to see some pay-back in the same coin.

Thus a plausible case, indeed a persuasive one, can be made for an SNP private preference for a UK Tory government and why French diplomats might want that to become public. It cannot be admitted in public, of course, but that seems to be the direction in which the facts of recent political history point.